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1
Content available Asymptotic analysis for coupled parabolic problem with Dirichlet-Fourier boundary conditions in a thin domain
Dilmi Mohamed
Journal of Mathematics and Applications
|
2023
|
Vol. 46
163--185
EN
This paper concerns the asymptotic behaviour of the initial boundary value problem of a class of reaction-diffusion systems (coupled parabolic systems) posed in a thin domain with Dirichlet-Fourier boundary conditions. We first prove the existence and uniqueness of the solution to the problem for fixed ε >0 by the Galerkin method. Then, we give the characterization of the limiting behaviour of these solution as the thinness tends to zero.
2
Content available On oscillatory behaviour of third-order half-linear dynamic equations on time scales
Grace Said R., Chhatria Gokula Nanda
Opuscula Mathematica
|
2022
|
Vol. 42, no. 6
849--865
EN
In this work, we study the oscillation and asymptotic behaviour of third-order nonlinear dynamic equations on time scales. The findings are obtained using an integral criterion as well as a comparison theorem with the oscillatory properties of a first-order dynamic equation. As a consequence, we give conditions which guarantee that all solutions to the aforementioned problem are only oscillatory, different from any other result in the literature. We propose novel oscillation criteria that improve, extend, and simplify existing ones in the literature. The results are associated with a numerical example. We point out that the results are new even for the case T = R or T = Z.
3
Content available On the stability of some systems of exponential difference equations
Psarros N., Papaschinopoulos G., Schinas C.J.
Opuscula Mathematica
|
2018
|
Vol. 38, no. 1
95--115
EN
In this paper we prove the stability of the zero equilibria of two systems of difference equations of exponential type, which are some extensions of an one-dimensional biological model. The stability of these systems is investigated in the special case when one of the eigenvalues is equal to -1 and the other eigenvalue has absolute value less than 1, using centre manifold theory. In addition, we study the existence and uniqueness of positive equilibria, the attractivity and the global asymptotic stability of these equilibria of some related systems of difference equations.
4
Content available Existence and asymptotic behavior of positive continuous solutions for a nonlinear elliptic system in the half space
Turki S.
Opuscula Mathematica
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2012
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Vol. 32, no. 4
783-795
EN
This paper deals with the existence and the asymptotic behavior of positive continuous solutions of the nonlinear elliptic system [formula] in the half space [formula] where α, β ≥ 1and r, s .≥ 0. The functions p and q are required to satisfy some appropriate conditions related to the Kato class [formula]. Our approach is based on potential theory tools and the use of Schauder's fixed point theorem.
5
Content available remote Oscillation properties of a class of nonlinear differential equations of neutral type
Tripathy A. K., Rao K V V S
Fasciculi Mathematici
|
2012
|
Nr 48
129--144
EN
Oscillatory and asymptotic behaviour of the solutions of a class of nonlinear rst order neutral delay dierential equa- tions with positive and negative coecients of the form E1 ...[wzór] are studied under various ranges of p(t). Sufficient conditions are obtained for the existence of positive bounded solution of (E2).
6
Content available remote Oscillation properties of a class of neutral differential equations with positive and negative coefficients
Tripathy A. K.
Fasciculi Mathematici
|
2010
|
Nr 45
133-155
EN
In this paper, oscillatory and asymptotic property of solutions of a class of nonlinear neutral delay differential equations of the form (E) ...[wzór] and ...[wzór] are studied under the assumptions ...[wzór] and ...[wzór] for various ranges of p(t). Sufficient conditions are obtained for existence of bounded positive solutions of (E).
7
Content available remote On a linear difference equation with several infinite lags
Čermák J.
Fasciculi Mathematici
|
2010
|
Nr 44
19-28
EN
This paper deals with asymptotic properties of the solutions of a variable order linear difference equation. As the main result, we derive the effective asymptotic estimate valid for all solutions of this equation. Moreover, we are going to discuss some consequences of this theoretical result, especially with respect to the numerical analysis of the multi-pantograph differential equation.
8
Content available remote Oscillation and non-oscillation criteria for a neutral delay difference equation of first order
Rath R., Rath S. K.
Fasciculi Mathematici
|
2009
|
Nr 42
109-120
EN
In this paper, necessary and sufficient condition are obtained so that every bounded solution of Δ(yn - yn-k) + qnG(yσ(n)) = 0 is oscillatory, under a condition weaker than ...[wzór]
9
Content available remote Oscillation and non-oscillation of neutral difference equations of first order with positive and negative coefficients
Rath R., Padhy L. N., Misra N.
Fasciculi Mathematici
|
2007
|
Nr 37
57-65
EN
In this paper necessary and sufficient conditions have been obtained so that every solution of the Neutral Delay Difference Equation (NODE) where different symbols have there usual meaning, oscillates or tends to zero as n → infin for different ranges of {pn}- This paper generalizes some recent work. The results of this paper hold for linear, sublinear or super linear equations and also for homogeneous equations, i.e. when fn equiv 0.
10
Content available remote Asymptotic behaviour of oscillatory solutions of n-th order differnetial equations
Padhi S.
Fasciculi Mathematici
|
2007
|
Nr 37
49-55
EN
In this paper, sufficient conditions have been obtained so that all oscillatory solutions of the n-th order differential equations with quasi derivatives tend to zero as t tends to infinity.
11
Content available remote Necessary and sufficient conditions for oscillation of solutions of a first order forced nonlinear difference equation with several delays
Rath R. N., Padhy L. N.
Fasciculi Mathematici
|
2005
|
Nr 35
99-113
EN
In this paper necessary and sufficient conditions have been obtained so that every solution of the Neutral Delay Difference Equation (NDDE) oscillates or tends to zero as n —> &infin for different ranges of This paper improves and generalizes some recent work [2. 6, 8]. The results of this paper hold for linear, sublinear and superlinear equations and also for homogeneous equations, i.e. when fn ≡ 0.
12
Content available remote Asymptotic behaviour of a discrete dynamical system generated by a simple evolutionary process
Karcz-Dulęba I.
International Journal of Applied Mathematics and Computer Science
|
2004
|
Vol. 14, no 1
79-90
EN
A simple model of phenotypic evolution is introduced and analysed in a space of population states. The expected values of the population states generate a discrete dynamical system. The asymptotic behaviour of the system is studied with the use of classical tools of dynamical systems. The number, location and stability of fixed points of the system depend on parameters of a fitness function and the parameters of the evolutionary process itself. The influence of evolutionary process parameters on the stability of the fixed points is discussed. For large values of the standard deviation of mutation, fixed points become unstable and periodical orbits arise. An analysis of the periodical orbits is presented.
13
Content available remote Oscillatory and asymptotic behavior of fourth order nonlinear delay difference equations
Graef J. R., Thandapani E.
Fasciculi Mathematici
|
2001
|
Nr 31
23-36
EN
The authors consider the nonlinear difference equation (E) delta2 ((delta(bn delta yn))+f(n,yn-t)=0, n należy N(no)={no,no+1,...}, here {an} and {bn} are positive real sequences, I is a nonnegative integer, f: N(no) x R R is a continuous function with uf(n, u) > 0 for all u nierówne 0. They obtain necessary and sufficient conditions for the existence of nonoscillatory solutions with a specified asymptotic behavior. They also obtain sufficient conditions for all solutions to be oscillatory if/ is either strongly sublinear or strongly superlinear. Examples of their results are also included.
14
Content available remote On asymptotic behaviour and oscillation of forced first order nonlinear neutral difference equations
Parhi N., Tripathy A. K.
Fasciculi Mathematici
|
2001
|
Nr 32
83-95
EN
Oscillatory and asymptotic behaviour of solutions of forced first order nonlinear neutral delay difference equations of the from (mathematical formula) is studied under appropriate assumptions on sequences of real numbers {qn} and {q(n) {f(n)} and {fn} and G belong to class C(R, R). The behaviour of solutions of mathematical formula is also discussed where {pa} is allowed to change sign.
15
Content available remote Existence of nonoscillatory solution for linear neutral delay equation
Kulenovic M. R. S., Hadziomerspahic S.
Fasciculi Mathematici
|
2001
|
Nr 32
61-72
EN
Consider the neutral delay differential equation with positive and negative coefficients (mathematical formula) where p s R and (mathematical formula) We obtain the sufficient condition for the existence of a nonoscillatory solution of the above equation to be (mathematical formula) and certain technical conditions implying thatdominates for large enough, for =-1.
16
Content available remote On nonlinear boundary value problem with a mixed nonhomogeneus condition: asymptotic behavior of solutions
Long N., Dung B., Nghia N., Thuyet T.
Demonstratio Mathematica
|
2001
|
Vol. 34, nr 3
609-618
17
Content available remote Asymptotic behavior of solutions of second order neutral difference equations with "maxima"
Luo J., Yu Y.
Demonstratio Mathematica
|
2001
|
Vol. 34, nr 1
83-89
EN
Second order neutral difference equations with "maxima" are considered and some asymptotic properties of nonoscillatory solutions are given.
18
Content available remote Growth estimate for solutions of difference equations
Popenda J., Radicheva E.
Fasciculi Mathematici
|
1999
|
Nr 30
147-158
EN
In the paper asymptotic estimates for nonoscillatory solutions of some kinds of difference equations are given.
19
Content available remote Asymptotic behaviour of solutions of higher order difference equations
Migda M.
Demonstratio Mathematica
|
1998
|
Vol. 31, nr 1
71-80
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